Functional it{\^o} versus banach space stochastic calculus and strict solutions of semilinear path-dependent equations

Functional It\^o calculus was introduced in order to expand a functional $F(t, X\_{\cdot+t}, X\_t)$ depending on time $t$, past and present values of the process $X$. Another possibility to expand $F(t, X\_{\cdot+t}, X\_t)$ consists in considering the path $X\_{\cdot+t}=\{X\_{x+t},\,x\in[-T,0]\}$ as an element of the Banach space of continuous functions on $C([-T,0])$ and to use Banach space stochastic calculus. The aim of this paper is threefold. 1) To reformulate functional It\^o calculus, separating time and past, making use of the regularization procedures which matches more naturally the notion of horizontal derivative which is one of the tools of that calculus. 2) To exploit this reformulation in order to discuss the (not obvious) relation between the functional and the Banach space approaches. 3) To study existence and uniqueness of smooth solutions to path-dependent partial differential equations which naturally arise in the study of functional It\^o calculus. More precisely, we study a path-dependent equation of Kolmogorov type which is related to the window process of the solution to an It\^o stochastic differential equation with path-dependent coefficients. We also study a semilinear version of that equation.Comment: This paper is a substantial improvement with additional research material of the first part of the unpublished paper arXiv:1401.503

Strong-viscosity Solutions: Semilinear Parabolic PDEs and Path-dependent PDEs

The aim of the present work is the introduction of a viscosity type solution, called strong-viscosity solution to distinguish it from the classical one, with the following peculiarities: it is a purely analytic object; it can be easily adapted to more general equations than classical partial differential equations. First, we introduce the notion of strong-viscosity solution for semilinear parabolic partial differential equations, defining it, in a few words, as the pointwise limit of classical solutions to perturbed semilinear parabolic partial differential equations; we compare it with the standard definition of viscosity solution. Afterwards, we extend the concept of strong-viscosity solution to the case of semilinear parabolic path-dependent partial differential equations, providing an existence and uniqueness result.Comment: arXiv admin note: text overlap with arXiv:1401.503

A regularization approach to functional It\^o calculus and strong-viscosity solutions to path-dependent PDEs

First, we revisit functional It\^o/path-dependent calculus started by B. Dupire, R. Cont and D.-A. Fourni\'e, using the formulation of calculus via regularization. Relations with the corresponding Banach space valued calculus introduced by C. Di Girolami and the second named author are explored. The second part of the paper is devoted to the study of the Kolmogorov type equation associated with the so called window Brownian motion, called path-dependent heat equation, for which well-posedness at the level of classical solutions is established. Then, a notion of strong approximating solution, called strong-viscosity solution, is introduced which is supposed to be a substitution tool to the viscosity solution. For that kind of solution, we also prove existence and uniqueness. The notion of strong-viscosity solution motivates the last part of the paper which is devoted to explore this new concept of solution for general semilinear PDEs in the finite dimensional case. We prove an equivalence result between the classical viscosity solution and the new one. The definition of strong-viscosity solution for semilinear PDEs is inspired by the notion of "good" solution, and it is based again on an approximating procedure

Calculus via regularizations in Banach spaces and Kolmogorov-type path-dependent equations

The paper reminds the basic ideas of stochastic calculus via regularizations in Banach spaces and its applications to the study of strict solutions of Kolmogorov path dependent equations associated with "windows" of diffusion processes. One makes the link between the Banach space approach and the so called functional stochastic calculus. When no strict solutions are available one describes the notion of strong-viscosity solution which alternative (in infinite dimension) to the classical notion of viscosity solution.Comment: arXiv admin note: text overlap with arXiv:1401.503

Knowledge-Intensive Processes: Characteristics, Requirements and Analysis of Contemporary Approaches

Engineering of knowledge-intensive processes (KiPs) is far from being mastered, since they are genuinely knowledge- and data-centric, and require substantial flexibility, at both design- and run-time. In this work, starting from a scientific literature analysis in the area of KiPs and from three real-world domains and application scenarios, we provide a precise characterization of KiPs. Furthermore, we devise some general requirements related to KiPs management and execution. Such requirements contribute to the definition of an evaluation framework to assess current system support for KiPs. To this end, we present a critical analysis on a number of existing process-oriented approaches by discussing their efficacy against the requirements

Davenant's The Law Against Lovers: Rewriting Shakespeare in early Restoration theatre

L'elaborato finale tratta uno dei primi adattamenti shakespeariani del periodo della restaurazione: The Law Against Lovers (1662, La legge contro gli amanti). L'opera, scritta da Sir William Davenant (figura chiave del teatro del periodo immediatamente precedente e successivo all'Interregno), adatta due opere del Bardo: Misura per misura e Molto rumore per nulla. Si analizzano qui le sue caratteristiche salienti, le innovazioni e le differenze rispetto ai due testi di partenza, sottolineando l'abilità di Davenant nello sfruttare gli elementi di successo del teatro (attrici, musica e danza, effetti scenici). Si traccia insomma una analisi mettendo in luce da una parte il contesto (letterario, teatrale, con le sue innovazioni, e politico), dall'altra l'operazione di Davenant sui testi di Shakespeare, che stravolge il senso originale, soprattutto da un punto di vista morale. This essay analyses The Law Against Lovers, a conflation of two Shakespearean works: Measure for Measure and Much Ado About Nothing. It is one of the very first adaptations of the Restoration period (1662), and one of the most peculiar, too. We highlight Davenant's ability to use the innovations of the theatre of the time (actresses, music and dance, theatrical effects) to achieve success (although in the end we cannot be sure whether this adaptation was actually successful). To conclude, one the one hand we have analysed the context of this adaptation (from a literary and also political perspective), and on the other hand we have analysed the changes carried out by Davenant to the two source texts, in order to prove that this adaptation is by no means «a sad puzzle» as some critics have said; it is instead a «good play», and a perfect example of the way Restoration adapters considered Shakespeare

Storie autobiografiche e autobiografia romanzata: traduzione e commento di alcuni racconti e dell'autobiografia di Arthur Machen

Questa tesi di laurea magistrale propone la traduzione di alcuni racconti fantastici e dell’autobiografia (Far Off Things) del gallese Arthur Machen (1863-1947). Dopo un breve sguardo alla biografia, alle opere, alla ricezione e fortuna dell’autore e alla sua poetica, il commento critico metterà in risalto prima le caratteristiche narratologiche e stilistiche dei racconti e poi l’importanza e i contenuti dell’autobiografia. Infine, il commento traduttologico evidenzierà i principali ostacoli alla traduzione di opere lontane dal lettore italiano d’oggi dal punto di vista sia temporale sia culturale

Feminism comes to campus: women at CSU 1960-1971

1994 Summer.Includes bibliographic references (pages 92-96).Covers not scanned.During the sixties students protested everything from restrictive social regulations to the Vietnam War. In this changing environment women, relying on skills learned in mainstream and protest activities, demanded changes for themselves. By the end of the decade these factors converged to foster the emergence of a feminist consciousness among some CSU women. In addition this thesis examines the important role of male student leaders, who had both a provocative and paternalistic relationship with women, in the development of feminism on campus. Relying upon the student newspaper, the CSU Collegian, oral interviews, and other university materials from that era I demonstrate the importance of the campus to the emergence of feminism in the sixties and early seventies. Chapter One examines the early protests of women and men against restrictive housing regulations and demonstrates that the fights against parietal rules was important for the formation of strategies and tactics that would be used later when feminists explicitly challenged gender-specific forms of university discrimination. Chapter Two explores how local and national events of the mid-sixties influenced women activists at CSU and nurtured a budding feminist consciousness on campus. Chapter Three, through an examination of women's organizations, shows that a feminist consciousness was clearly present on campus by 1968